Question

Relation between electric potential gradient and electric field

Answer 1

Electric field can exist only if there is a difference in potential.

Potential, however high, if it is equal at all points, there will be no electric field.

Thus, in general Electric field is defined as negative space derivative of potential.

Considering one dimensional case for simplicity,

E = - dV/dx

Or E= - (gradient of potential)

(-) sign indicates that field is directed from higher potential to lower potential.